Newtons Laws (III)
Newtons
Blocks on ramps, and other problems
Serway and Jewett : 5.7, 5.8
Doing problems with F=ma
Draw the free-body diagram carefully.
You may need to know the direction of a from
kinematics, before considering forces (for friction)
Lecture 9
Newtons Laws applied to systems with two or more accelerated bodies.
Serway and Jewett : 5.7, 5.8
Physics 1D03 - Lecture 9
1
Problems with several accelerated objects:
Free-body diagram for each object. Relate forces by finding action-reaction
Newtons Laws (III)
Blocks on ramps, and other problems
Serway and Jewett : 5.7, 5.8
Physics 1D03 - Lecture 8
1
Doing problems with F=ma
Draw the free-body diagram carefully. You may need to know the direction of a from kinematics, before considering for
Rotation (III)
Rotation
Torque and angular acceleration
Moment of inertia
Text Sections : 10.7, and part of 10.4
Angular velocity vector: parallel to the axis
of rotation, following a similar right-hand rule:
rotation
direction
Angular acceleration vect
Rotation of a Rigid Body (Chapter 10)
Each particle travels in a circle. The speeds of the particles differ, but each one completes a full revolution in the same time.
We describe the rotational motion using angle, angular velocity, and angular accelerati
Circular Motion
Circular
Newtons Second Law and circular motion
Serway and Jewett 6.1, 6.2
Review: Circular Motion Kinematics
a has components
dv
i) at =
, rate of change of speed
dt
v2
ii) ac =
, from change in direction
r
a
center
radial component, ac
Torque
Torque in 2 and 3 dimensions
Text Sections : 10.6
Physics 1D03 - Lecture 10
1
Torque is what causes rotation
An unbalanced force applied
to an object causes it to move
(accelerate).
F
a
Even with no net force, the
object is not necessarily in
equi
0612345
Versionnumber
Multiple-choice answer sheets:
J.P.Student
HB pencil only; ink will not work
Fill circle completely
No extra marks in answer area
Erase well to change an answer
Rotational Dynamics
Rotational
Examples involving
Parallel-axis theorem
Work and Kinetic Energy
Work by a variable force
Kinetic Energy and the Work-Energy Theorem
Power
Serway & Jewett 7.3, 7.4
Determine the work done by a force as the
particle moves from x=0 to x=6m:
F(N)
5
x(m)
01
2
3456
Kinetic Energy
Definition: for a pa
Power; Rotational Energy
Power
Rotational work, power, and kinetic energy.
Serway & Jewett 7.5, 10.4, 10.8
Recall:
s = r
vt = r
at = r
f = i + ti
f = i + i t + 1 2 t 2
2 = i2 + 2
f
Power
Power is the rate at which work is done:
Average power = Work/tim
Static Equilibrium
(Serway 12.1-12.3)
Equilibrium of a Rigid Body
For a particle, Equilibrium means Fnet = 0, and then v = constant.
For extended 2-D or 3-D objects, this is not enough!
F1
Here
F = 0 , so aCM = 0.
But the object is not in equilibrium:
It
Work !
Review of scalar product of vectors
Work by a constant force
Work by a varying force
Example: a spring
Serway & Jewett 7.1 7.3
Work and Energy
Work
Newtons approach:
F = ma
- acceleration at any instant is caused by forces
Energy approach: Net wor
Potential Energy
Work and potential energy
Conservative and non-conservative forces
Gravitational and elastic potential energy
Conservation of Mechanical Energy
Serway and Jewett 8.1 8.3
mg
Gravitational Work
To lift the block to a height y
requires work
Kinematics in Two Dimensions
Position, velocity, acceleration vectors Constant acceleration in 2-D Free fall in 2-D Serway and Jewett : 4.1 to 4.3
Physics 1D03 - Lecture 4
1
The Position vector r points from the origin to the particle.
y
path
yj
r
xi
(
Newtons Laws (II)
Free-body diagrams Normal Force Friction, ropes and pulleys
Serway and Jewett : 5.7, 5.8
Physics 1D03 - Lecture 7
1
Free-Body Diagrams
Pick one object (the body). Draw all external forces which act directly on that body (gravity, conta
If you missed the first lecture. . .
Find the course webpage:
http:/physwww.mcmaster.ca/~okon/1d03/1d03.html
and read the course outline and the first lecture.
Log into Avenue to Learn (http:/avenue.mcmaster.ca)
and find Physics 1D03. There you can find
Lecture 9
Newtons Laws applied to systems with two or
more accelerated bodies.
Serway and Jewett : 5.7, 5.8
Physics 1D03 - Lecture 9
1
Problems with several accelerated objects:
Free-body diagram for each object.
Relate forces by finding action-reactio
Circular Motion
Circular
Newtons Second Law and circular motion
Serway and Jewett 6.1, 6.2
Review: Circular Motion Kinematics
a has components
i) at =
dv
, rate of change of speed
dt
v2
ii) ar =
, from change in direction
r
a
center
radial component, ar
Rotation of a Rigid Body (Chapter 10)
Each particle travels in a circle.
The speeds of the particles
differ, but each one completes
a full revolution in the same
time.
We describe the rotational motion using angle,
angular velocity, and angular accelerati
Torque
Torque in 2 and 3 dimensions
Text Sections : 10.6
Physics 1D03 - Lecture 10
1
Torque is what causes rotation
An unbalanced force applied
to an object causes it to move
(accelerate).
F
a
Even with no net force, the
object is not necessarily in
equi
Rotation (III)
Rotation
Torque and angular acceleration
Moment of inertia
Text Sections : 10.7, and part of 10.4
Angular velocity vector: parallel to the axis
of rotation, following a similar right-hand rule:
rotation
direction
Angular acceleration vect
0612345
Versionnumber
Multiple-choice answer sheets:
J.P.Student
HB pencil only; ink will not work
Fill circle completely
No extra marks in answer area
Erase well to change an answer
Rotational Dynamics
Rotational
Examples involving
Parallel-axis theorem
0612345
Versionnumber
Multiple-choice answer sheets:
J.P.Student
HB pencil only; ink will not work
Fill circle completely
No extra marks in answer area
Erase well to change an answer
Centre of Mass
Centre of Mass, Centre of Gravity
Serway 12.1-12.2; and
Static Equilibrium
(Serway 12.1-12.3)
Equilibrium of a Rigid Body
For a particle, Equilibrium means Fnet = 0, and then v = constant.
For extended 2-D or 3-D objects, this is not enough!
F1
Here
F = 0 , so aCM = 0.
But the object is not in equilibrium:
It
Vectors
Scalars and Vectors Vector Components and Arithmetic Vectors in 3 Dimensions Unit vectors i, j, k
Serway and Jewett Chapter 3
Physics 1D03 - Lecture 3
1
Physical quantities are classified as scalars, vectors, etc. Scalar : described by a real num
Kinematics in 2-D (II)
Uniform circular motion Tangential and radial components of a Relative velocity and acceleration Serway and Jweett : 4.4 to 4.6
Physics 1D03 - Lecture 5
1
Uniform Circular Motion
v uniform means constant speed velocity v changes (
Newtons Laws of Motion
Newtons Laws Forces Mass and Weight Serway and Jewett 5.1 to 5.6
Physics 1D03 - Lecture 6
1
Newtons First Law (Law of Inertia)
An isolated object, free from external forces, will continue moving at constant velocity, or remain at r
Energy Examples
Serway and Jewett 8.1 8.3
Conservative Forces
B
path 1
A force is called conservative
if the work done (in going from
some point A to B) is the same
for all paths from A to B.
A
path 2
W1 = W2
An equivalent definition:
For a conservative f
Energy
Potential energy
Examples with rotation
Force and Potential Energy
Serway 8.4-8.6; 10.8
Mechanical Energy
E = K + U = K + Ugravity + Uspring + .
Mechanical energy is conserved by conservative
forces; the total mechanical energy does not change if
o
Chen Cheng
RLST 1637
Prof. Turpeinen
3/28/2017
The Bubble of Experience in Tibetan Buddhism
The idea of experience in Tibetan Buddhism has always been an interesting topic to not
only scholars in academia but also to practitioners of Buddhism in the west.